1. Field
This invention relates to instructional material for physically demonstrating concepts of mathematics. More particularly, the invention is an apparatus adapted for aiding students to visualize geometric and trigonometric shapes and the angular relationships therebetween.
2. State of the Art
The use of toys, games and visual aids to teach students has long been recognized as a beneficial means to draw interest and as a memory device to help students retain abstract concepts. Likewise, any method or apparatus which is enjoyable for a student tends to motivate during a student's own study or practice time. Visualization contributes to improved retention of abstract principles. A clear explanation is very difficult to achieve with mere words when discussing mathematical principles and geometric relationships. Nevertheless, diagrams and figures drawn by a teacher on a board or presented in textbooks have only limited ability to attract interest and lack any interaction with the student to investigate and discover the operation of the principles presented. Numerous inventions have been developed which allow a student to experiment, or a child to play, or a teacher to drill. Many of the devices which are available to teach geometric and mathematical principles are limited in their ability to teach general principles. No device in the cited art addressed the more sophisticated concepts equivalent to high school mathematical course work.
Geometric shapes known within the toy art. For example, U.S. Pat. No. 4,183,167 (Jatich, issued Jan. 15, 1980) shows a board having rows of pegs on which geometric shapes of triangles, squares, circles or hexagons can be placed to make a variety of designs and to intermesh with each other. Similarly, U.S. Pat. No. 3,849,912 (Kemnitzer, issued Nov. 26, 1974) discloses an educational toy having a board provided with rows of vertical pegs on which a variety of circular, triangular and rectangular shapes can be fit and stacked. U.S. Pat. No. 3,766,667 (Glassman, issued Oct. 23, 1973) describes a system of dowels and blocks which can be stacked to demonstrate the equivalence of additive values between blocks marked according to relative length. U.S. Pat. No. 3,302,311 (Israel, issued Feb. 7, 1967) describes vertical dowels on a base to receive square cubes marked with patterns on their outer surfaces so as to create a variety of patterns depending upon the location and orientation of each of the blocks. Triangular blocks are disclosed as well. U.S. Pat. No. 2,611,193 (Davis, issued Sep. 23, 1952) describes a circular base plate for an "arithmetic fraction trainer," having numerous vertical pegs on which sectors of a circle can be placed to show how fractions such as two halves, three thirds, four quarters, etc. add to make a whole circle. A design-forming toy is disclosed in U.S. Pat. 2,759,295 (Keuls, issued Aug. 21, 1956) having a base plate containing a grid of apertures into which a multiplicity of shapes can be inserted by means of a central post on each shape.
A variety of shaped building block toys and mosaic inlay systems have also resulted from the educational model, game and toy art. One of the earliest is U.S. Pat. No. 510,178 (Konig, issued Dec. 5, 1893) comprising a base board having conical depressions on an even grid spacing, which depressions each may receive a mosaic piece shaped to fit complementarily therein to form a mosaic surface pattern. The edges of colored mosaic pieces fit snugly to form the top visible surfaces. U.S. Pat. No. 3,487,579 (Brettingen, issued Jan. 6, 1970) describes interlocking blocks of hexagonal shape having hexagonal pegs on one side thereof and recesses in the opposing side thereof such that the blocks can be stacked one on top of another and at various angles with respect to each other to form a variety of designs. U.S. Pat. No. 3,570,170 (Kishi, issued Mar. 16, 1971) describes a rectangular block having pegs of circular cross section on one side thereof, the opposing side containing recesses to receive the pegs, thus promoting an ability to stack the blocks snugly together at a variety of translational locations and at 90.degree. orientations within the plane of the surfaces containing the pegs and recesses.
U.S. Pat. No. 3,579,859 (Malenge, issued May 25, 1971) discloses an educational game in which the user arranges a number of colored shapes on a plane to obtain figures and patterns by placing round elements, or cylindrical elements, or rectangular elements on a variety of grid locations to create a mosaic-like effect. Also, the invention describes various designs which can be made by revealing different colored sheets through grid openings overlying them. U.S. Pat. No. 3,748,752 (Quercetti, issued Jul. 31, 1973) discloses a mosaic block which can be interlocked with other identical mosaic blocks to make a surface, or a pattern, or a figure.
U.S. Pat. No. 4,051,621 (Hogan, issued Oct. 4, 1977) discloses a set containing a variety of "homohedral" modules which have pegs and openings at their vertices which can fit together to construct more elaborate structures.
All the foregoing toys, games and models rely on numerous manufactured pieces of regular shape and of considerable bulk to demonstrate a limited number of shapes and relations. Likewise, each of the shapes used is limited in its ability to teach the underlying principles of mathematics which relate to shapes, lines, angles and other interrelationships.
Thus, the aids, toys, and games in the art restrict a teacher or a student to the limited choice of manufactured shapes that are available with the device. Likewise, little experimentation is available, and no capability to extend understanding to more complex or generalized principles such as those encountered in a math class, particularly at a junior high or high school level.